United have not commented on the extent of the Belgian international's problems, but the 26-year-old is on crutches with his left foot in a protective cast.
Fellaini had been expected to tie up a loan move to Serie A club Napoli before the end of the transfer window but that move is clearly now in doubt.
New United boss Louis Van Gaal has made it clear he does not see a future for Fellaini at Old Trafford despite mounting injury problems at the club.
Fellaini's midfield partner Michael Carrick is already ruled out for around two months with an ankle injury, leaving Ander Herrera and Darren Fletcher as United's only fit central midfielders.
Other players currently out through injury for United include Tom Cleverley, Antonio Valencia, Luke Shaw, Jonny Evans and Danny Welbeck which gives van Gaal a headache as he looks to rebound from last weekend’s defeat to Swansea at Sunderland on Sunday.
Fellaini has endured a disappointing career at Old Trafford since his £27.5million move on transfer deadline day last summer.
The former Everton player has yet to score a competitive goal for the club and has made just 16 starts due to a combination of poor form and injuries.
He was booed by some United fans after coming on as a substitute during the pre-season win over Valencia at Old Trafford before scoring a late winning goal.
Fellaini also appeared as a substitute in Saturday's Premier League defeat to Swansea, replacing Herrera for the last 23 minutes of the match.